Answers
Given:
A figure of dilation and the center of dilation is O.
To find:
The value of y.
Solution:
The distance between center and vertex of image (d') is proportional to the distance between center and the corresponding vertex of original figure (d).
[tex]d'\propto d[/tex]
[tex]d'=kd[/tex]
[tex]\dfrac{d'}{d}=k[/tex]
Where, k is the scale factor or constant of proportionality.
So, the scale factor for the given dilation is
[tex]k=\dfrac{OB'}{OB}[/tex]
[tex]k=\dfrac{36}{16}[/tex]
[tex]k=\dfrac{9}{4}[/tex]
We know that,
[tex]k=\dfrac{\text{Side length of image}}{\text{Corresponding side length of original figure}}[/tex]
[tex]\dfrac{9}{4}=\dfrac{A'C'}{AC}[/tex]
[tex]\dfrac{9}{4}=\dfrac{27}{y}[/tex]
[tex]9\times y=27\times 4[/tex]
Divide both sides by 9.
[tex]y=\dfrac{27\times 4}{9}[/tex]
[tex]y=3\times 4[/tex]
[tex]y=12[/tex]
Therefore, the value of y is 12.
Related Questions
3x − y = 10
4x + 19y = 18
no solution? One solution? or infinitely solutions
Answers
Answer:
Infinite
Step-by-step explanation:
find the value of a and b if 1/5+√7= a+b√7
Answers
Answer:
[tex]a=\dfrac{1}{5}[/tex] and b = 1
Step-by-step explanation:
Given that,
[tex]\dfrac{1}{5}+\sqrt7=a+b\sqrt7[/tex]
We need to find the value of a and b.
We should compare both sides of the above equation i.e.
[tex]a=\dfrac{1}{5}[/tex]
and
b = 1
Hence, the values of a and b are 1/5 and 1 respectively.
Please help ASAP. Thanks so much.
Answers
Answer:
D. 1/9
Step-by-step explanation:
The x-coordinate is -1/3
The 2 line segments form a ___ that helps us find the ___
Answers
Answer:
is this on shapes or multiple answer?
Step-by-step explanation:
like i was thinking 2 segments as parallel
Find the circumference of the circle below. Use 3.14 pi. Round your answer to the nearest tenth.
12.1
12.6
25.1
50.2
PLEASE EXPLAIN HOW YOU GOT YOUR ANSWER!!!
Answers
Step-by-step explanation:
radius = 4 inches π = 3.14circumference = 2π × radius = 2 × 3.14 × 4 = 25.1 inches _________________________FOLLOW MEAnswer:25.1
Step-by-step explanation:
Select the correct answer.
Use this tax table to find how much tax you need to pay on a taxable income of $40,000.
The tax is:
If taxable
income is over-
But not
over-
SO
$7,825
$31,850
$77,100
$7.825 10 percent of the
amount over SO
$31,850 $782.50 plus 15 percent
of the amount over
7,825
$77,100 $4,386.25 plus 25
percent of the amount
over 31,850
$160,850 $15,698.75 plus 28
percent of the amount
over 77.100
$349.700 $39,148.75 plus 33
percent of the amount
over 160,850
no limit S101,469.25 plus 35
percent of the amount
over 349.700
S160,850
S349,700
OA
$6,423.75
OB
$8.150.50
OC. $12.536.25
Reset
Net
Reset
Next
Answers
A. Grace spent P184.35 for a box of chocolates and
handkerchiefs. She gave her sister P125.00. The money she had left was
P127.75? How much did she have at first?
1. What is asked in the problem?
2. What are the given facts?
3. What is the operation to be used?
4. What is the number sentence?
5. What is the solution?
Answers
Step-by-step explanation:
1. What is asked in the problem?
How much did she have at first?
2. What are the given facts?
- Grace spent P184.35 for a box of chocolates and handkerchiefs
- She gave her sister P125.00.
- The money she had left was P127.75
3. What is the operation to be used?
Addition
5. What is the solution?
Initial amount = Money spent on Choc and handkerchiefs + Money she gave her sister + Amount left
Initial Amount = P184.35 + P125.00 + P127.75
Initial Amount = P437.1
plssss helppp!!!!!!!!!
Answers
Answer:
17. x=25
18. x=72
19. x=151
20. x=28
Step-by-step explanation:
Pythagorean theorem
please help
Answers
Answer:
c = square of a2+b2
i think its correct ome
which set of number are right for this inequality x<14 plz help me i need help due in 20 min
A. 3,7,9,10,12
B. 15, 18 ,20, 21, 23
C. 17, 21, 24, 25, 31
D. 23, 27, 29, 30, 36
Answers
Answer:
it's A because all of those numbers are less than 14
Step-by-step explanation:
Sujan bought 16 pens for Rs256. how much would he have to pay for one pen he buys next time?
Answers
Step-by-step explanation:
.......................
Answer:
Rs 16
Step-by-step explanation:
Amount of money paid for 16 pens = Rs 256
Amount of money paid for 1 pen =
[tex] \frac{256}{16} = \frac{128}{8} \\ = \frac{64}{4} = \frac{32}{2} \\ = \frac{16}{1} \\ [/tex]
Therefore, amount paid for one pen is Rs 16
how to find (a) and (b)?
Answers
Answer:
A) Gradient = -3
B) 3y - x = 7
Step-by-step explanation:
The curve has the equation;
y = x³ - 6x² + 9x + 1
We are given the pints it passes through as;
A(2,3) and P(3, 1)
A) to find the gradient, we will find the derivative of the given equation.
Thus;
Gradient = y' = 3x² - 12x + 9
At point A, x = 2. Thus;
Gradient = 3(2²) - 12(2) + 9
Gradient = 12 - 24 + 9
Gradient = -3
B) since the gradient of the tangent = -3, it means the gradient of the normal will be; -1/-3 = 1/3
Thus, equation of the normal to the curve at point A will be;
(y - 3) = ⅓(x - 2)
Multiply both sides by 3 to get;
3y - 9 = x - 2
3y - x = 9 - 2
3y - x = 7
Write an equivalent expression. 4x - x
Answers
Answer:
5x-2x
Step-by-step explanation:
4x-x = 3x
so,
5x-2x = 3x
The equivalent expression would be; 5x-2x
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
We are given that the expression as; 4x - x
We need to find an equivalent expression.
Therefore, solving further;
4x-x = 3x
Thus, we can also create one expression as;
5x-2x = 3x
Learn more about expression here;
https://brainly.com/question/14083225
#SPJ2
HELP ME PLEASE I HAVE 1 MINUTE LEFT TO TRUN THIS IN
Answers
Answer:
1jdjsbsjsnsisn Shane Jana aus she sue euw
Answer:
Number of walnut trees: 4n+15
1. There are 4 quarts in 1 gallon. How many quarts are in 4 ½ gallons?
Answers
Answer:
18 quarts
Step-by-step explanation:
A rectangle has sides 10 and 8. Find the length of the Diagonal
Answers
Answer:
Step-by-step explanation:
Remark
The diagonal is found by using the Pythagorean Theorem: a^2 + b^2 = c^2. This only works for certain figures. The rectangle is one of them.
Givens
a = 10
b = 8
c = ? This is the length of the diagonal.
Solution
a^2 + b^2 = c^2
10^2 + 8^ = c^2
100 + 64 = c^2
c^2 = 164
√c^2 = √164
c = 12.806
There are 5,000 books in the town's library. Of these,4,400 are fiction. To find the percent of the books that are fiction, first set up the percent equation. Then find the percent. Setup the percent equation. Choose the correct answer below. A. m B. m C. m Your answer is not correct.D. m This is the correct answer. nothing% of the books are fiction
Answers
Answer:
4,400=m•5,000 and 88%
If f(x)= 1/2x-10+3, which inequality can be used to find the domain of f(x)?
Answers
Answer:
x ≠ 5
Step-by-step explanation:
Assuming you mean f(x) = (1/(2x-10))+3
Please be careful with how ambigiuous your question can appear with the / sign.
The domain is the set of values that can be used as an input.
In this case the only input we have that could cause problem is if the denominator of the fraction is 0, because then we divide by 0 which is not allowed.
This gives us 2x-10 ≠ 0
2x ≠ 10
x ≠ 5
The domain of the function is given by the inequality ( 1/2 )x - 10 ≥ 0 and the value of x ≥ 20
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = [ √ ( 1/2 )x - 10 ] + 3
Now , the expression (1/2)x - 10 inside the square root must be greater than or equal to 0, as the square root of a negative number is not defined in the real number system.
(1/2)x - 10 ≥ 0
To solve this inequality, we can isolate x:
(1/2)x ≥ 10
x ≥ 20
Hence , the domain of the function f(x) is x ≥ 20.
To learn more about domain and range click :
https://brainly.com/question/28135761
#SPJ7
The complete question is attached below :
If f(x)= 1/2x-10+3, which inequality can be used to find the domain of f(x)?
4y=5x-1 3x-2y=1 solve each system using substitution
Answers
Answer:
(1,1)
x=1 y=1
Step-by-step explanation:
When you solve by substitution, you have to isolate each equation Hope this helps.
if x+y=5, then what does y-5 equal?
Answers
Answer:
-x
Step-by-step explanation:
rearrange the terms by adding or subtracting the same thing from both sides:
[tex]x+y=5\\y = 5 - x\\y - 5 = -x[/tex]
33 Calculaţi, dând factor comun:
a 26*(-12) +26 (-18) + 26.40;
c (-18) (-22) + (-18) (-36) + (-18) - 8;
b 15*(-34) - 15*21 +15*35;
d -26* (-12) - 26*(-18) - 26*40.
Cu rezolvare nu doar rezultatul
Answers
Răspuns:
260; 1188; -300; - 260
Explicație pas cu pas:
A.)
26 * (- 12) +26 (-18) + 26,40;
26 (- 12 - 18 + 40)
26 (10)
= 260
C.)
(-18) (-22) + (-18) (-36) + (-18) - 8;
-18 (- 22 - 36 - 8)
-18 (-66)
= 1188
b.)
15 * (- 34) - 15 * 21 + 15 * 35;
15 (-34 - 21 + 35)
15 (- 20)
= - 300
d.)
-26 * (-12) - 26 * (- 18) - 26 * 40.
-26 (- 12 - 18 + 40)
-26 (10)
-260
if Rohans weight is t+6 kg and is 7 kg less than Rahul whose weight is 54 kg. What is the value of t
Answers
Answer:
T = 41
Step-by-step explanation:
Rohan's weight = t+6
Rahul's Weight = t+6+7 = 54
t = 54 - 6 - 7
t = 41
One number added to twice another number is 30. The sum of the numbers is 19.
Write and solve a system of equations to represent this situation.
What is the value of the smaller number?
What is the value of the larger number?
I don't understand :(
Answers
Answer:
The smaller number is 8
The bigger number is 11
Step-by-step explanation:
let the first number be A
let the second number be B
A + 2B = 30..... equation 1
A + B = 19...... equation 2
Subtract equation 2 from 1.
A + 2B = 30
- A + B = 19
-------------------
0 + B = 11
B = 11
Substitute B = 11 into equation 2
A + B = 19
A + 11 = 19
collect like terms
A = 19-11
A = 8.
A= 8 and B = 11
4. A regular hexagon is shown below. Find the value of x. (11x + 21)
Answers
Answer:
We need the picture
Step-by-step explanation:
The logarithm of the base to it self is always......
Answers
Answer:
Step-by-step explanation:
Logₐa = 1
Answer:
positive that is 1
Step-by-step explanation:
While the value of a logarithm itself can be positive or negative, the base of the log function and the argument of the log function are a different story.
The argument of a log function can only take positive base arguments. In other words, the only numbers you can plug into a log function are positive base numbers as it is always 1.
What is 75% converted to a decimal? mal?
Answers
Answer:
75% = 0.75
Step-by-step explanation:
75% ÷ 100 = 0.75
Answer:
.75
Step-by-step explanation:
75.% you move the the point 2 spaces to the front and get .75
17. **4• 2 = (3 x 100 000) + (2 x 10 000)+
(8 x 1 000) + (4 x 100) + (2x1)
Yukandaki eşitliğe göre (* + %) - ( + ) işle-
minin sonucu kaçtır?
A. 9
B.8
C. 7.
D. 6
Answers
Cevap:9 umarım doğrusunu seçersin
what are the equal factors to 10 to the second power
Answers
Answer:
100 i think
Step-by-step explanation:
Answer:
inequality 1 has a solution of 5
Step-by-step explanation:
Today is the birthday of Rahul and he is 3 times
as old as Nirmala. In 13 years, Rahul will be one
year less than twice as old as Nirmala will be
then. The age of Rahul today is:
a. 30 years
c. 49 years
b. 36 years
d. 30 years
Answers
Answer:
b. 36 years
Step-by-step explanation:
Today
Nirmala = x years
Rahul = 3x years
In 13 years
Nirmala = 3x + 13 years
Rahul = 2(x+13) - 1
3x + 13 = 2(x+13) - 1
3x + 13 = 2x + 26 - 1
3x + 13 = 2x + 25
3x - 2x = 25 - 13
x = 12
Nirmala = x years
= 12 years
Rahul = 3x years
= 3(12)
= 36 years
The age of Rahul today is 36 years
Sam says: 9.05kg is equal to 9500g. Is he right or wrong? Explain your answer.
Answers
Answer:
Step-by-step explanation:
Sam is wrong because 9,05 kg =9050g which is different to 9500g
Answer:
wrong 1 kilo in a gram is 1000 so u just going to add 1 zero on the back so 905+0= 9050 grams